### JDQZ method for the generalized eigenvalue problem

Posted:

**Tue Jul 28, 2015 4:50 am**Are you looking at the JDQZ for MAGMA? This is a method for the solution of the generalised eigenvalue problem for a small no of eigenvalues.

It uses GMRES and optionally BiCGstab internally.

I was recommended to look at it and have only recently found the code at http://www.win.tue.nl/casa/research/sci ... tware.html

I have it working on my CPU for a small case (about 4000 square). It works quite well for up to 6 or 7 eigenvalues with a preconditioner of A-1 (via factorisation).

The results I get agree with Arpack for the same problem.

I have now been able to track down the following article here http://www.staff.science.uu.nl/~sleij101/JD_software/

References: D. R. Fokkema, G. L. G. Sleijpen, H. A. van der Vorst

Jacobi-Davidson style QR and QZ algorithms for the reduction of matrix pencils.

SIAM J. Sci. Comput., 20(1):94-125, 1998.

I hope this is of interest.

John

It uses GMRES and optionally BiCGstab internally.

I was recommended to look at it and have only recently found the code at http://www.win.tue.nl/casa/research/sci ... tware.html

I have it working on my CPU for a small case (about 4000 square). It works quite well for up to 6 or 7 eigenvalues with a preconditioner of A-1 (via factorisation).

The results I get agree with Arpack for the same problem.

I have now been able to track down the following article here http://www.staff.science.uu.nl/~sleij101/JD_software/

References: D. R. Fokkema, G. L. G. Sleijpen, H. A. van der Vorst

Jacobi-Davidson style QR and QZ algorithms for the reduction of matrix pencils.

SIAM J. Sci. Comput., 20(1):94-125, 1998.

I hope this is of interest.

John